How to precompute and supply a parameter-dependent 2D boundary lifting field (Robin BCs) in PyBaMM?

[poonia-git]

Hi PyBaMM team,

I’m working on a custom x-lumped (y–z) thermal submodel for a pouch cell based on a Chebyshev–Galerkin reduced formulation (DOI: doi.org/10.1109/TPEL.2020.3027561). The approach introduces a boundary “lifting” temperature field $T_e(y,z)$ that satisfies heterogeneous Robin boundary conditions on the four edges (left/right/top/bottom may have different heat transfer coefficients). The reduced model then evolves only the coefficient states $a_k(t)$, with the temperature reconstructed as
$T(y,z,t)=T_e(y,z)*T_\infty(t)+\sum_k a_k(t)\psi_k(y,z),$
and with face cooling handled in the usual x-lumped form (i.e., proportional to $T-T_{\text{surf}})$.

To keep runtime low, I’d like to precompute $T_e(y,z)$ once (or once per parameter set) and inject it into the model, rather than solving an auxiliary boundary-value problem repeatedly during time integration. What’s the recommended PyBaMM pattern for this kind of precomputation, which involves parameter inputs from the user?

Thanks!

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